Supplementary Figure 2 Photoluminescence in 1L- (black line) and 7L-MoS 2 (red line) of the Figure 1B with illuminated wavelength of 543 nm.

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1 PL (normalized) Intensity (arb. u.) L-MoS 1L-MoS Raman shift (cm -1 ) Supplementary Figure 1 Raman spectra of the Figure 1B at the 1L-MoS area (black line) and 7L-MoS area (red line). In the analysis of the Raman spectra of 1L- MoS, the peak at 384 cm 1 corresponds to the in-plane (E 1 g) mode, while that at 43 cm 1 is attributed to the out of plane (A 1g ) mode 1,. The freuency difference bsetween these two modes of 19 cm 1 observed in the Raman spectrum in Figure S1 can be used as a measure of 1L-MoS 1. The E 1 g mode softens, and A 1g mode stiffens with increasing layer thickness, similar to other layered materials, where the bond distance changes with the number of layers 3. The peak of Raman spectra of 7L-MoS appeared at 381 cm 1 (E 1 g) and 46 cm 1 (A 1g ) with a freuency difference of 5 cm -1. This difference can also vary as a function of doping L-MoS 3 7L-MoS Wavelength (nm) Supplementary Figure Photoluminescence in 1L- (black line) and 7L-MoS (red line) of the Figure 1B with illuminated wavelength of 543 nm.

2 Supplementary Figure 3 Schematics of photocarrier extraction mechanisms for a, bulk TMD and b, 1L-TMD heterostructures. Supplementary Figure 4 a, Cross-sectional bright-field STEM image of MoS on graphite. b, Calculated electrostatic potentials of 1L-MoS heterostructures and in the vacuum environmental condition. Green colored areas indicate the potential energy barrier. Supplementary Figure 5 Raman spectra of the top (Gr T, black line), bottom (Gr B, red line) graphene and overlapped area (blue line) in Figure 1b.

3 3 Supplementary Figure 6 Schematic images of electrostatic potentials of 1L-MoS heterostructures before and after graphene doping. Supplementary Figure 7 Sliced suare barriers with width of.1 nm for tunnelling probability calculation.

4 4 Supplementary Figure 8 a and b, I-V characteristics of (a) graphene/1l- MoS /graphene and (b) graphene/multi-layer MoS /graphene at the various V g under dark state. Supplementary Figure 9 a and b, Simulated band diagram of (a) graphene/1l- MoS /graphene and (b) graphene/multi-layer MoS /graphene at the negative V g (red line) and positive V g (black line). Supplementary Note 1 The absorption spectra of MoS was determined from the reflectance measurements 4,5. To obtain the absorption spectrum, the reflectance spectrum from the 1L and 6L-MoS flake on a glass substrate (R m+s ) and that from the same bare glass substrate (R s ) were measured using an optical microscope coupled with a spectrometer and CCD camera. The fractional change in the reflectance, δ R, can be determined as the difference of these two uantities divided by the reflectance from the bare glass substrate ( ). The absorbance of MoS (A) can then be determined by using the relation: sub, where n sub is the refractive index of the glass substrate. Rm s R Rs R s 4 R A n 1 Supplementary Note The dielectric constant of graphene is determined by the standard approximation 6,7 of ε Gr = (ε below + ε above)/, where ε below is the dielectric constant of the material below

5 5 graphene and ε avobe is the dielectric constant of the material above graphene. If the device is in the vacuum (condition for DFT), the dielectric constant for 1L-MoS heterostructure is ε Gr = (ε 1L-MoS + ε vacuum )/ =.7, where ε 1L-MoS = Figure S6b shows calculated electrostatic potential of van der Waals heterostructure device in the vacuum environment, which is highly convinced to the DFT calculated electrostatic potential (Fig. 1E). Supplementary Note 3 D peaks are observed at 7 in Gr B and 716 cm -1 in Gr T. The D band shift is the evidence of the charge doping in graphene from due to the phonon stiffening 9. With n-/p-type doping, D peak of the graphene shifts in the downward/upward directions, respectively. Top graphene is more p-type doped than bottom graphene caused by different environmental reasons 1. In the overlapping area, two distinctive peaks are observed that merged Gr B and Gr T peaks. It means that the doping densities in top and bottom graphenes are maintained in this overlapping area. Supplementary Note 4 Electrostatic potential including environmental conditions is calculated by considering Coulomb interaction of top- and bottom-graphene in different dielectric constant with MoS layer. In the atomic system, the electron (-charge) and nucleus (+charge, protons) are attracted to each other by Coulomb force. The Coulomb force between electron (-) and protons (+Z) is ( )( Z) F 4 r [Supplementary euation 1] where r is the distance between the electron, Z is atomic number, and is the permittivity of free space. Because the force F on a particle is eual to minus the gradient of the potential energy, the potential energy for the one electron is simply Z E( r) ( F) dr 4 r [Supplementary euation ] The excited electron is further from the nucleus than the core electrons in the valence band. In effect, the negatively charged core electrons screen the excited electron from the full +Ze charge of the nucleus. The excited electron would see only a net

6 6 charge of +e, and other +(Z-1)e charges are completely screened by core electrons 11. Then the potential energy for the excited electron can be written as E( r) 4 r [Supplementary euation 3] When two nuclei are allowed to approach each other, then electron would be influenced by both nuclei according to Coulomb s law. The electron potential energy of a single electron at any point is now E p r 4 ( r a) 4 [Supplementary euation 4] where r is the distances between the electron and nuclei, and a is the distance between two nuclei. The electrostatic potential of graphene/1l-mos /graphene can be calculated by E p r 4 ( r.676nm) 4 [Supplementary euation 5] where each term is for bottom graphene, MoS (sulfur, molybdenum, sulfur), and top graphene respectively. Typical distance of.154 nm between sulfur and molybdenum in MoS was used. The distance between graphene and MoS was measured to.83 nm by ross-sectional bright-field scanning transmission electron microscope (STEM) images (Fig. S5a). In order to include the environmental conditions (graphene doping condition), dielectric constant of bottom graphene, MoS (sulfur, molybdenum, sulfur), and top graphene can be used [Supplementary euation 6] ( r.83nm) 4 ( r.984nm) 4 ( r 1.66nm) 4 E p 4 GrB r 4 MoS ( r.676nm) 4 MoS ( r.83nm) 4 MoS ( r.984nm) 4 GrT ( r 1.66nm) For the electrostatic potential calculation of multi-layer MoS heterostructures, multiple MoS layers can be simply added between bottom and top graphene layers. In the Thomas Fermi screening, electrons in a solid can deform the coulomb potential by electric field screening. Thomas Fermi screening wavevector is given by

7 7 in 3 dimentional materials (Supplementary euation 7) in dimentional materials (Supplementary euation 8) Where g s is spin degeneracy, g v is valley degeneracy, n is electron concentration, e is the elementary charge, k is dielectric constant, is plank constant, v F is Fermi velocity, and m is electron mass, which can deform the Coulomb potential by limits the screening length (or, euivalently, the Debye length of ) 1. The euations indicates that the Coulomb potential can be deformed depend on carrier concentration (n) in 3 dimentional materials (thick multi-layer materials), while the Coulomb potential is independent on carrier concentration (n) in dimentional materials (thin few-layer materials). Supplementary Note 5 The excited carrier continuity euation is d dt d n D dx d n n n g dx [Supplementary euation 9] Where δn is excited carrier density in unit volume (cm 3 ), D is the diffusion coefficient, μ is the mobility, is the built-in internal electric field, τ is the excited carrier lifetime, and g is the generation rate of carriers 13. In steady state, the euation is d dt d d n n D n n g [Supplementary euation 1] dx dx If we assume that the most of photons are adsorbed at the surface, and there is no generation of carriers in inner MoS, then g =. The euation can then be reduced to d d 1 n n n [Supplementary euation 11] dx D dx D General solution for this euation is n x Ae 1 D D 4 x D [Supplementary euation 1]

8 8 where nx is the excited carrier density at a moving distance of x nm by diffusion and drift, and A is an unknown coefficient. If we use n as an initial excited carrier concentration at the surface (x = nm), then n A. The excited carrier concentration at a moving distance x ( nx ) is n x 1 4 x D D D n e [Supplementary euation 13] The excited carriers are decayed exponentially by the recombination as the increasing the moving distance (x) increases by diffusion and drift. The diffusion coefficient (D) of MoS to the vertical direction is obtained by Einstein relation of D [Supplementary euation 14] k T where the k B is the boltzmann constant, T is the temperature, and μ is electron mobility of MoS along the vertical direction. Supplementary Note 6 The configurations of graphene/mos /graphene (GMG) is considered in our simulation work. We adapt the depletion approximation, which means MoS is uniformly charged, and the charge density euals its doping level. Therefore, bands of MoS are parabolic instead of linear. This model is reasonable when the device channel is short, as in our cases. For the simulation of GMG, we consider the electric field induced by gate as E g, and then we have E V / D [Supplementary euation 15] g g where V g is the gate voltage and D is the thickness of SiO dielectric. Then we consider electric fields in the two grapheme-mos interfaces as E 1 and E. The carrier density n 1 and n for bottom graphene and top graphene, respectively, can be given by: E E n e [Supplementary euation 16] l g s E s 1 1 n e [Supplementary euation 17] where 1 and are the dielectric constant for SiO and MoS, respectively. B

9 9 E 1 and E satisfy: Ned E1 E [Supplementary euation 18] s where N is the doping level in MoS. In our simulation, N is chosen to be 1 17 cm -3, which can be roughly estimated from transported characteristics of MoS used in our study. If we have E 1 and E, we can get the potential drop ΔV in MoS as: 1 V ( E1 E ) d [Supplementary euation 19] For graphene, we have the relation between carrier density n and chemical potential μ (Dirac point as zero) as: h v F n n [Supplementary euation ] where h is the plank constant and v F is the Fermi velocity, n is the fixed charge graphene. Supplementary References 1. Lee, C. et al. Anomalous lattice vibrations of single- and few-layer MoS. ACS Nano 4, 695 (1).. Zhang, X. et al. Raman spectroscopy of shear and layer breathing modes in multilayer MoS. Phys. Rev. B 87, (13). 3. Arenal, R. et al. Raman spectroscopy of single-wall boron nitride nanotubes. Nano Lett. 6, 181 (6). 4. Chakraborty, B. et al. Symmetry-dependent phonon renormalization in monolayer MoS transistor. Phys. Rev. B 85, (1). 5. Williams, R. H. & Mcevoy, A. J. Photoemission studies of MoS. Phys. Stat. Sol. (b) 47, 17 (1971). 6. Hwang, C. et al. Fermi velocity engineering in graphene by substrate modification. Sci. Rep. 5:59 (1).

10 1 7. Elias, D. C. et al. Dirac cones reshaped by interaction effects in suspended graphene. Nat. Phys. 7, 71 (11). 8. Chen, X. et al. Probing the electron states and metal-insulator transition mechanisms in molybdenum disulphide vertical heterostructures. Nat. Comm. 6:688 (15). 9. Das, A. et al. Monitoring dopants by raman scattering in an electrochemically topgated graphene Transistor. Nat. Nanotechnol. 3, 1-15 (8). 1. Britnell, L. et al. Field-effect tunneling transistor based on vertical graphene heterostructures. Science 335, (1). 11. Livingston, J. D. Electronic properties of engineering materials. Wiley & Sons, Inc., New York, (1999). 1. Sarma, S. D., Adam, S., Hwang, E. H. & Rossi, E. Electronic transport in twodimensional graphene. Rev. Mod. Phys. 83, (11). 13. Sze, S. M. & Ng, K.K. Physics of Semiconductor Devices. Wiley, New York, (7).